Biologically Inspired Achromatic Waveplates for Visible Light

ARTICLE

Received 10 Mar 2011 | Accepted 19 May 2011 | Published 21 Jun 2011 DOI: 10.1038/ncomms1358 Biologically inspired achromatic waveplates for visible light

Yi-Jun Jen1, Akhlesh Lakhtakia2, Ching-Wei Yu1, Chia-Feng Lin1, Meng-Jie Lin1, Shih-Hao Wang1 & Jyun-Rong Lai1

Waveplates are planar devices used in optics and optoelectronics to change the polarization state of light. Made of anisotropic dielectric materials such as crystals and thin films, waveplates are not known to exhibit achromatic performance over the visible regime. Inspired by the microvillar structure of R8 cells functioning as polarization converters in the eyes of stomatopod crustaceans, we conceived, designed, fabricated and tested periodically multilayered structures comprising two different types of arrays of nanorods. Morphologically analogous to the ocular cells, here we show that the periodically multilayered structures can function as achromatic waveplates over the visible regime.

1 Department of Electro-Optical Engineering, National Taipei University of Technology, No. 1, Sec. 3, Chung-Hsiao E. Road, Taipei 106, Taiwan. 2 Materials Research Institute and Department of Engineering Science & Mechanics, Pennsylvania State University, University Park, Pennsylvania 16802, USA. Correspondence and requests for materials should be addressed to A.L. (email: [email protected]) or to Y.-J.J. (email: [email protected]). nature communications | 2:363 | DOI: 10.1038/ncomms1358 | www.nature.com/naturecommunications © 2011 Macmillan Publishers Limited. All rights reserved. ARTICLE nature communications | DOI: 10.1038/ncomms1358

he tip of the electric field vector of a light wave vibrates in a b 1.56

a plane, describing a figure that can vary in shape from a x 1.54 straight line to a circle to an ellipse. Accordingly, light is said 1.52

T e inde to be either linearly polarized or circularly polarized or, in general, 1.50 elliptically polarized. Elliptically polarized light has two linearly 1.48 z polarized components, the electric field vectors of which are mutu- Refractiv 1.46 ally orthogonal and can have a phase difference. For any polarization x 1.44 y 400 450 500 550 600 650 700 state, another polarization state can be found such that the two are Wavelength (nm) mutually orthogonal. The conversion of one polarization state into another is a key manipulation in optical science and engineering. Figure 1 | The structure and equivalent refractive indexes of a serial

A waveplate alters the polarization state of light passing through bideposited Ta2O5 nanorod array. (a) Cross-sectional scanning electron it by creating a relative phase between the linearly polarized micrograph of an array of upright Ta2O5 nanorods produced using the components1–3. A typical waveplate is a plate made of an anisotropic SBD method. Each collimated vapour produced a 5-nm growth, the total dielectric material4—either a natural crystal such as calcite and quartz2 thickness of the nanorod array being 174 ± 5 nm. Scale bar, 100 nm. 5,6 or a thin film —which displays birefringence, by presenting differ- (b) Equivalent refractive indexes nx (red line) and ny (blue line) of this ent refractive indexes to the two linearly polarized components of array in the visible regime. incident light7. The difference in the two refractive indexes, being wavelength z dependent in general, leads to wavelength-dependent retardation of x the phase of one polarization state in relation to that of the orthogo- y nal polarization state. But a desirable waveplate must transmit light of a fixed polarization state uniformly over a broad range of wave- lengths. Achromatic performance requires the waveplate to be made 1 Period of a material whose intrinsic optical properties compensate other (ABA) wavelength-dependent effects. Furthermore, the transmittance must be sufficiently high and weakly dependent on the wavelength for a waveplate to be useful. Achromatic waveplates are needed for three-dimensional dis- Upright nanorods (layer A) 8 9 plays and CD/DVD readers , among several optical applica- Tilted nanorods (layer B) tions. But a suitable quartz waveplate, besides being fragile due to ~15-µm thickness, exhibits considerable variation in phase retarda- Figure 2 | Schematic of a unit cell ABA. Cross-sectional SEM of a unit cell tion over the entire visible regime (400–700 nm wavelength range)10, ABA with a thickness of 246 ± 5 nm. Scale bar, 100 nm. Layer A comprising and elaborate designs are needed even for partial success10–14. upright nanorods and layer B comprising tilted nanorods form the unit cell A recent study has demonstrated the presence of achromatic of a periodic multilayered structure. waveplates in the eyes of stomatopod crustaceans of species Odon- todactylus scyllaru15. Comprising many eyelets or ommatidia, each compound eye of such stomatopod crustaceans can distinguish the chosen for both OAD and SBD methods because its refractive index left-handed or right-handed circular polarized light that is emit- is almost constant over the visible regime, and also it is chemically ted as a sexual signal from a male or female15. The key to this dis- and thermally stable21–24. crimination is the exceptionally sophisticated morphology of the R8 cell of each ommatidium. An array of aligned microvilli in the R8 Results cell functions as a quarter waveplate, better than engineered wave- Birefringence of a serial bideposited film. Figure 1a shows a cross- plates10. The effective birefringence displayed by the microvillar array section scanning electron micrograph (SEM) of a 174 ± 5-nm thin has two components: intrinsic birefringence of the microvilli mate- film comprising upright nanorods fabricated with the SBD method. rial and form birefringence from the aciculate (that is, needle-like) Both collimated vapours of Ta2O5 were directed at an angle θν = 75° geometry of the microvilli. The subwavelength optical architecture with respect to the normal (z axis) to the substrate plane (xy plane). of the cellular structure thus integrates two dispersive mechanisms The cross-sectional dimensions of the nanorods being much smaller for birefringence to deliver a wavelength-independent phase retar- than the wavelength, the thin film is an optical continuum that dation over the visible regime. Fabrication of this subwavelength presents an equivalent refractive index nx to normally incident light nanostructure could yield achromatic waveplates (and other optical whose electric field vector vibrates along thex axis, but the equivalent devices) for operation throughout the visible regime. refractive index changes to ny when that electric field vector vibrates A biologically inspired artificial achromatic waveplate designed along the y axis. Figure 1b shows the wavelength dependences of nx and fabricated as a periodic multilayer structure (PMS) with a unit and ny , obtained by fitting these two parameters to measured data cell made of two different nanorod arrays fabricated with two differ- on optical transmittance25,26. The nanorod array is thus effectively ent physical vapour deposition methods5,16–18 is reported here. The birefringent, and the weak dependence of the refractive index 5,16 first method, called the oblique angle deposition (OAD) method , difference ny − nx of the chosen material (Ta2O5) on the wavelength requires the production of a collimated vapour that collects on a over the 400–700 nm range simplifies the design of achromatic planar substrate as an array of parallel and tilted nanorods owing to waveplates. a self-shadowing effect. This array of nanorods is effectively a dielectric thin film, which is biaxially anisotropic, because the nanorods Periodic multilayered structures. For that purpose, the achromatic are aciculate and have non-circular cross-section17,18. The second waveplate was conceived as a PMS, as shown in Figure 2. The unit method is called the serial bideposition (SBD) method, wherein two cell comprising three layers, with two layers labelled A sandwiching collimated vapors are produced sequentially and sufficiently rapidly a layer labelled B, is symmetric. Layers labelled A are to be fabri- so that the nanorods are upright18–20; hence, the thin film exhibits an cated using the SBD method, with both collimated vapours oriented enhanced refractive index difference in relation to the one produced in the xz plane. Layers labelled B are to be fabricated using the OAD 19,20 with only one collimated vapour . Tantalum oxide (Ta2O5) was method with just a single collimated vapour oriented in the yz plane.

nature communications | 2:363 | DOI: 10.1038/ncomms1358 | www.nature.com/naturecommunications © 2011 Macmillan Publishers Limited. All rights reserved. nature communications | DOI: 10.1038/ncomms1358 ARTICLE

The anisotropic optical properties of layers A and B are represented as a b i 5 polarization-dependent refractive indexes nj (i = A, B; j = x, y). For normally incident light, a symmetric unit cell is equivalent 4 to a homogeneous layer of refractive index nE and phase thickness E j 3 g (which is 2π times the product of the refractive index and the j 2 thickness divided by the wavelength for a homogeneous thin film)5; the superscript E stands for equivalent. A PMS comprising m identi- 1 cal symmetric unit cells is equivalent to a homogeneous layer with Phase retardation (deg) 0 E E 400 450 500 550 600 650 700 a refractive index nj and phase thickness mg j . The PMS reflects E Wavelength (nm) strongly in a wavelength regime called the stop band, wherein nj has an imaginary part. Outside the stop band, nE is real and the c d j 12 1.0 PMS can be transparent in a wavelength regime called a pass band. 0.8 E E 11 0.6 The parameters nj and g j are two different functions of wave- 0.4 A B 0.2 length and four other parameters (nj , nj , dA and dB). The relation- E E 10 0.0 ship between nj and g j departs from the simple linear relationship –0.2 9 es parameters –0.4 for a homogeneous thin film. For an achromatic waveplate, the –0.6 AB, Stok –0.8 parameters nx, y and dA,B have thus to be realized in such a way that 8 –1.0 E E Phase retardation (deg) the phase retardation m()gy − g x is independent of the wavelength; 400 450 500 550 600 650 700 400 450 500 550 600 650 700 i i Wavelength (nm) Wavelength (nm) specifically, the differencesn x − ny do not have to be linearly propor- tional to the wavelength. The aciculate morphology of the waveplate Figure 3 | Achromatic waveplate with a three-cell PMS. (a) Calculated is optically similar to the microvillar array in R8 cells of stomatopod E E crustaceans, and the form birefringences of the two different types spectrum of the phase retardation gy − g x of the unit cell ABA on glass. of layers in the unit cell ABA of the PMS can be combined to achieve (b) Cross-sectional SEM of a PMS of three unit cells, the calculated optical achromatic phase retardation. properties of each unit cell being presented in (a). Scale bar, 100 nm. (c) Measured spectrum of the phase retardation of the three-cell PMS on glass. (d) Measured spectra of the four Stokes parameters S (red line), Three-cell PMS achromatic waveplate. For this study, layers A 0 S (black line), S (green line) and S (blue line) of the light transmitted by and B were first independently deposited. The thicknesses of layers 1 2 3 A and B were controlled to be 48 ± 2 and 150 ± 2 nm, respectively, the three-cell PMS of (b), when the incident light is linearly polarized at and the average cross-sectional diameters of the nanorods were 45° to the x axis in the xy plane. A A 26 ± 2 nm. By varying θν from 65° to 80°, (nx , ny ) were experimen- tally found to vary from (1.663, 1.788) to (1.396, 1.451) at 632.8 nm wavelength. Likewise, at the same wavelength (nB, nB) varied from x y z (1.816, 1.792) to (1.458, 1.431) when θν was varied from 60° to 80°. Layer C: isotropic x i film (28 nm) The parameterized dependences ofn j on θν at 632.8 nm wavelength y were determined as follows: A 3 2 nx =0..00013qν − 0 02732 qν +1.91800qν − 42.73200,65° < qν <80 ° (1) 23 periods 23 (ABA) A 3 2 n = −0..00009q+0 02044 q −1.50927q + 39.16300,65°

B 3 2 Figure 4 | Schematic of a 23-cell PMS with an index-matching layer at ny = −0..00001qν +0 00086 qν − 0..05181qν +3 09114,50 °

These relationships were used for designing PMS. For fabricating a PMS, θν was chosen as 75° for layer A so that The polarization state of light is comprehensively captured by A A 27 (nx , ny ) = (1.453, 1.547) at 632.8 nm wavelength; likewise, θν was four quantities called the Stokes parameters . For normally inci- B B chosen as 70° for layer B so that (nx , ny ) = (1.662, 1.636) at the same dent light that is linearly polarized at 45° to the x axis in the xy plane, wavelength. The calculated phase retardation of the unit cell ABA the Stokes parameters of the light transmitted by the three-cell on glass is 3.35 ± 0.52° in the visible regime, as shown in Figure 3a. PMS were measured over the visible regime. As shown in Next, a PMS made of m = 3 unit cells ABA was fabricated on a glass Figure 3d, all four Stokes parameters are remarkably uniform over (BK7) substrate, and the phase retardation was measured over the vis- the 400–700 nm wavelength range, thereby confirming the achro- ible regime. Figure 3b shows a cross-sectional SEM of the fabricated maticity of the three-cell PMS. PMS, and Figure 3c shows that the phase retardation is 10.41 ± 1.16° over the 400–700 nm wavelength regime. The phase retardation is 23-cell PMS achromatic waveplate. Although the phase retardation thrice the value predicted in Figure 3a for a single unit cell, and the of the three-cell PMS is 10.41°, higher values of the phase retardation achromaticity of the three-cell PMS compares favourably with that can be realized by cascading several different PMS′s. Alternatively, a reported for the R8 cells of stomatopod crustaceans (for which the single m-cell PMS with high m can be designed. Figure 4 shows the phase retardation has a ± 2.7° variation10). Furthermore, the maxi- design of a 23-cell PMS that is predicted to deliver a phase retarda- mum variation in the phase retardation does not increase as fast as m. tion of 89.33° in the visible regime. Each ABA unit cell comprises nature communications | 2:363 | DOI: 10.1038/ncomms1358 | www.nature.com/naturecommunications © 2011 Macmillan Publishers Limited. All rights reserved. ARTICLE nature communications | DOI: 10.1038/ncomms1358

a b insensitivity of the transmittance to the polarization state and the x 2.8 140 wavelength of incident light. 2.6 120 2.4 e inde 2.2 100 Methods 2.0 80 Electron beam evaporation. For the SBD method, two collimated vapours of 1.8 60 1.6 Ta2O5 were produced by electron-beam impingement of two Ta2O5 targets in a 40 vacuum chamber, wherein the base pressure was 4×10 − 6 Torr. The vapours were

alent refractiv 1.4 20 1.2 directed onto a glass substrate (BK7) at an average angle θν with respect to the nor- Phase retardation (deg)

Equiv 1.0 0 mal (z axis) to the substrate plane (xy plane), the sources of the collimated vapours 400 450 500 550 600 650 700 400 450 500 550 600 650 700 being located on opposite ends of the x axis in the xz plane. Each source was Wavelength (nm) Wavelength (nm) located at 30 cm from the centre of the substrate plane. The cross-sectional dimen- c 100 d 1.0 sions of the substrate were 21 mm×23 mm. The OAD and SBD methods usually 90 29 ) 0.8 80 produce thin films with uniformity at these length scales . The deposition rate was 0.6 − 1 70 0.4 typically 0.3 nm s . For the OAD method, only one of the two targets was used. 60 0.2 50 0.0 Optical measurements 40 –0.2 . With linearly polarized incident light, the transmittance

30 es parameters –0.4 was measured using the VASE ellipsometer (J.A. Woollam Co.). Both the phase ansmittance (% 20 –0.6

Tr retardation and the Stokes parameters of the transmitted light were also measured 10 Stok –0.8 0 –1.0 with the same equipment. 400 450 500 550 600 650 700 400 450 500 550 600 650 700 All optical measurements were performed at the centre of the sample, as well as Wavelength (nm) Wavelength (nm) at two points diametrically apart from the centre at a distance of 10 mm from each other. The spectra of phase retardation and the Stokes parameters of the transmit- Figure 5 | Achromatic waveplate with a 23-cell PMS. (a) Computed ted light at either of those two points on a three-cell PMS shifted by about 10 nm E E with respect to their counterparts obtained at the centre of the sample, thereby spectra of nx and ny of the unit cell ABA presented in Figure 4. (b) Computed spectrum of the phase retardation of a 23-cell PMS on glass. indicating acceptable uniformity over a circular area of 10 mm diameter. The substrate dimensions can be scaled up if the distance between the vapour source and (c) Computed transmittance spectra of the device presented in Figure 4. the centre of the substrate is also increased proportionally16, and uniformity over (d) Computed spectra of the four Stokes parameters S0 (red line), S1 (black larger length scales can be realized in scaled-up systems. line), S2 (green line) and S3 (blue line) of the transmitted light of the device With the angle of incidence varying over a ± 5° range from normal incidence, presented in Figure 4, when the incident light is linearly polarized at 45° to the phase retardation was found to vary < 1%. the x axis in the xy plane. Measurements were made repeatedly at 22 °C and 24% relative humidity. The phase retardation remained the same from 2 to 72 h after fabrication. Using a sensi- tive polarization conversion method30, we found that all three principal refractive

indexes of a Ta2O5 thin film did not vary from 1 to 144 h after fabrication. layers of type A (dA = 53 nm, θν = 78°) and B (dB = 149 nm, θν = 73°). Layer C, made of SiO2, was added at the entry pupil. References E E Calculated spectra of nx and ny of the unit cell ABA are shown 1. King, R. J. Quarter-wave retardation systems based on the Fresnel rhomb in Fig. 5a. The phase retardation of a single unit cell on glass is principle. J. Sci. Instrum. 43, 617–622 (1966). 3.97 ± 0.57° over the visible regime. The calculated spectrum 2. Ghatak, A. Optics Sec. 18.6 (Tata McGraw–Hill, 1989). 3. Born, M. & Wolf, E. Principles of Optics 6th edn, Sec. 14.4.2 (Cambridge of the phase retardation of the 23-cell PMS on glass is shown in University Press, 2002). Figure 5b. The phase retardation is 89.33 ± 6.83° over the visible 4. Mackay, T. G. & Lakhtakia, A. Electromagnetic Anisotropy and Bianisotropy regime, with a maximum variation less than thrice that of the R8 (World Scientific, 2010). cell of a stomatopod crustacean10. 5. Macleod, H. A. Thin-Film Optical Filters, 2nd edn. (Adam Hilger, 1986). 6. Baumeister, P. W. Optical Coating Technology (SPIE Press, 2004). Finally, an isotropic index-matching layer of SiO2 (layer C: C C 7. Pancharatnam, S. Achromatic combinations of birefringent plates. Part II. dC = 28 nm, ny = nx = 1.457 at 632.8 nm wavelength) was added at An achromatic quarter-wave plate. Proc. Ind. Acad. Sci. A 41, 137–144 the entry pupil, as shown in Figure 4. The calculated transmittance (1955). spectra for both linear polarization states, shown in Figure 5c, 8. Brennesholtz, M. S. & Stupp, E. H. Projection Displays, 2nd edn (John Wiley & are very close to each other. Computed spectra of the four Stokes Sons, 2008). 9. Wang, J. J. et al. High performance 100 mm-in-diameter true zero-order parameters presented in Figure 5d confirm achromaticity over the waveplates fabricated by imprint lithography. J. Vac. Sci. Technol. B 23, visible regime. 2950–2953 (2005). By providing index-matching layers28 at the entry pupil of an 10. Roberts, N. W., Chiou, T.- H., Marshall, N. J. & Cronin, T. W. A biological m-cell PMS, the overall transmittance can be made very high and quarter-wave retarder with excellent achromaticity in the visible wavelength quite independent of the polarization state of incident light, as region. Nat. Photon. 3, 641–644 (2009). 11. Kikuta, H., Ohira, Y. & Iwata, K. Achromatic quarter-wave plates using the shown in Figure 5. Thus, the achromatic arrangement can be used dispersion of form birefringence. Appl. Opt. 36, 1566–1572 (1997). as a drop-in device to change the polarization state of light. 12. Bokor, N., Shechter, R., Davidson, N., Friesem, A. A. & Hasman, E. Achromatic phase retarder by slanted illumination of a dielectric grating with period Discussion comparable with the wavelength. Appl. Opt. 40, 2076–2080 (2001). Our study has established achromatic phase retardation over 13. Yi, D.- E., Yan, Y-. B., Liu, H.- T., Si-Lu & Jin, G.- F. Broadband achromatic phase retarder by subwavelength grating. Opt. Commun. 227, 49–55 the visible regime—an extremely rare optical property hitherto (2003). reported only in the eyes of a certain stomatopod crustacean and 14. Yu, W., Mizutani, A., Kikuta, H. & Konishi, T. Reduced wavelength-dependent never before realized artificially—in a PMS with a symmetric unit quarter-wave plate fabricated by a multilayered subwavelength structure. Appl. Opt. 45, 2601–2606 (2006). cell fashioned from layers of upright and tilted Ta2O5 nanorods. The artificial bioinspired device can be used to change the polarization 15. Chiou, T.- H. et al. Circular polarization vision in a stomatopod crustacean. Curr. Biol. 18, 429–434 (2008). of light over the entire visible range. Achromatic waveplates can be 16. Lakhtakia, A. & Messier, R. Sculptured Thin Films: Nanoengineered Morphology similarly realized for operation in different wavelength regimes. and Optics, Chap. 3 (SPIE Press, 2005). The fabrication technique for the PMS is a workhorse tech- 17. Motohiro, T. & Taga, Y. Thin film retardation plate by oblique deposition. nique in the thin-film industry5,6, does not require expensive Appl. Opt. 28, 2466–2482 (1989). lithography equipment12,13, and is compatible with planar technol- 18. Hodgkinson, I. & Wu, Q. H. Serial bideposition of anisotropic thin films with enhanced linear birefringence. Appl. Opt. 38, 3621–3625 (1999). ogy commonplace in electronics and optoelectronics industries. 19. Hodgkinson, I. J., Wu, Q. H., Silva, L. D. & Arnold, M. Inorganic positive Further optimization will reduce the maximum variation in phase uniaxial films fabricated by serial bideposition.Opt. Express 12, 3840–3847 retardation over the visible regime, without compromising the (2004).

20. Pursel, S. M. & Horn, M. W. Prospects for nanowire sculptured thin-film 30. Jen, Y.- J., Peng, C.- Y. & Chang, H.- H. Optical constant determination of an ani- devices. J. Vac. Sci. Technol. B 25, 2611–2615 (2007). sotropic thin film via polarization conversion.Opt. Express 15, 4445–4451 (2007). 21. Sobahan, K. M. A., Park, Y. J. & Hwangbo, C. K. Effect of deposition angle on

the optical and the structural properties of Ta2O5 thin films fabricated by using glancing angle deposition. J. Korean Phys. Soc. 55, 1272–1277 (2009). Acknowledgments 22. Qi, H., Xiao, X., He, H., Yi, K. & Fan, Z. Optical properties and microstructure This work was supported by grants from the National Taipei University of Technology,

of Ta2O5 biaxial film.Appl. Opt. 48, 127–133 (2009). the National Science Council of the Republic of China (NSC 99-2221-E-027-043-MY3 23. Chaneliere, C., Autran, J. L., Devine, R. A. B. & Balland, B. Tantalum pentoxide and NSC 99-2120-M-002-012), and the Charles Godfrey Binder Endowment at the

(Ta2O5) thin films for advanced dielectric applications.Mater. Sci. Eng. R 22, Pennsylvania State University. 269–322 (1998). 24. Ezhilvalavan, S. & Tseng, T. Y. Preparation and properties of tantalum Author contributions pentoxide (Ta O ) thin films for ultra large scale integrated circuits (ULSIs) 2 5 Y.J.J. conceived the design and supervised the fabrication of the periodic multilayered application—a review. J. Mater. Sci. Mater. Electron 10, 9–31 (1999). structures. A.L. conducted a meta-analysis on all experimental and computational data. 25. Arndt, D. P., Azzam, R. M., Bennett, J. M., Borgobno, J. P. & Carniglia, C. K. C.W.Y. constructed the optical set-up and analysed the data. C.F.L. and M.J.L. measured Multiple determination of the optical constants of thin-film coating materials. and fabricated the PMS samples. S.H.W. and J.R.L. participated in experiments. Y.J.J. and Appl. Opt. 23, 3571–3596 (1984). A.L. wrote the manuscript. 26. Kim, S.- H. & Hwangbo, C. K. Influence of Ar ion-beam assistance and

annealing temperatures on properties of TiO2 thin films deposited by reactive DC magnetron sputtering. Thin Solid Films 475, 155–159 (2005). Additional information 27. Jackson, J. D. Classical Electrodynamics, 3rd edn, Sec. 7.2 (Wiley, 1999). Competing financial interests: The authors declare no competing financial interests. 28. Dhungel, S. K., Yoo, J., Kim, K., Jung, S., Ghosh, S. & Yi, J. Double-layer Reprints and permission information is available online at http://npg.nature.com/ antireflection coating of MgF /SiN for crystalline silicon solar cells. J. Korean 2 x reprintsandpermissions/ Phys. Soc. 49, 885–889 (2006). 29. Wang, J., Shao, J., Yi, K. & Fan, Z. Layer uniformity of glancing angle How to cite this article: Jen Y.-J. et al. Biologically inspired achromatic waveplates for deposition. Vacuum 78, 107–111 (2005). visible light. Nat. Commun. 2:363 doi: 10.1038/ncomms1358 (2011).